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A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies

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  • Guanxing Fu
  • Ulrich Horst
  • Xiaonyu Xia

Abstract

We consider a mean-field control problem with c\`adl\`ag semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and that it is of linear-quadratic form and that its coefficients satisfy a coupled system of non-standard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a sequence of discrete-time models. A sophisticated transformation shows that the system can be brought into standard Riccati form from which we deduce the existence of a global solution. Our analysis shows that the optimal strategy jumps only at the beginning and the end of the trading period.

Suggested Citation

  • Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies," Papers 2207.00446, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2207.00446
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    References listed on IDEAS

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    8. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    9. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
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    11. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2020. "C\`adl\`ag semimartingale strategies for optimal trade execution in stochastic order book models," Papers 2006.05863, arXiv.org, revised Jul 2021.
    12. Gârleanu, Nicolae & Pedersen, Lasse Heje, 2016. "Dynamic portfolio choice with frictions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 487-516.
    13. Christopher Lorenz & Alexander Schied, 2012. "Drift dependence of optimal trade execution strategies under transient price impact," Papers 1204.2716, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Xinman Cheng & Guanxing Fu & Xiaonyu Xia, 2024. "Long Time Behavior of Optimal Liquidation Problems," Papers 2405.14177, arXiv.org.
    2. Robert Denkert & Ulrich Horst, 2024. "Extended mean-field games with multi-dimensional singular controls and non-linear jump impact," Papers 2402.09317, arXiv.org.

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